Conditional Generative Adversarial Network Based on Self-Attention Mechanism and VAE Algorithm and Its Applications

2.1 The current state of research on financial data based on GANs

Financial/financial data is a type of data signal with strong data attributes. research on financial/financial data generation and identification based on GANs is emerging, Innovations primarily focused on the application of GANs in this domain to address data generation, data identification, and data-assisted decision-making challenges. The main research areas include:

Takahashi et al. [17] proposed "Modeling financial time-series with Generative Adversarial Networks" to address the statistical mechanisms underlying financial time series modeling. This method leverages Generative Adversarial Networks (GANs) to learn the data characteristics and generate realistic data in a data-driven manner. The time series generated by the GAN model can restore the statistical properties of financial time series. Experimental results confirm the feasibility of this approach. To address the issue of financial fraud detection, represented by credit card fraud, Zhao et al. [18] proposed a self-attention-based Generative Adversarial Network model (SAGANs) in "Advancing financial fraud detection: Self-attention Generative Adversarial Networks for precise and effective identification." To optimize and improve fraud detection algorithms, the model extracts key features and patterns from large-scale transaction datasets, deepening the mathematical abstraction of credit card fraud data and enhancing the accuracy of identification. To address the issue of systematic trading strategy optimization, Koshiyama et al. [19] proposed "Generative Adversarial Networks for financial trading strategies fine-tuning and combination" and developed a complete methodology based on training and selection of cGAN, single-sample strategy calibration, and multi-sample generative modeling. Experiments show that the algorithm provides a feasible and effective approach to solving the problem of systematic trading strategy optimization. In "DeepPricing: pricing convertible bonds based on financial time-series Generative Adversarial Networks," Tan et al. [20] proposed a novel data-driven convertible bond pricing model, DeepPricing, which effectively addresses the pricing problem of convertible bonds. The algorithm introduces a new type of financial time-series Generative Adversarial Network (FinGAN) to generate risk-neutral stock return processes that preserve the original statistical properties. This allows the model to capture the dynamic changes of the underlying stock return process while retaining the rich characteristics of the convertible bond market. Experimental results show that the proposed algorithm outperforms traditional methods in convertible bond pricing. Lin et al. [21] proposed an efficient credit default swap (CDS) prediction model based on Generative Adversarial Networks in "Credit default swap prediction based on Generative Adversarial Networks" to enhance the intelligence of credit risk management and provide investors with more accurate risk management and trading strategy support. In their paper Fin-GAN: Forecasting and Classifying Financial Time Series via Generative Adversarial Networks, Vuletić et al. [22] proposed a specialized adversarial neural network with an improved loss function to explore the application of Generative Adversarial Networks (GANs) in financial time series probabilistic forecasting. This network effectively solves the challenges associated with applying GANs in this context. Experimental results demonstrate that the model surpasses traditional supervised learning models in terms of the Sharpe ratio. To explore the similarity between synthetic data sequences generated by Wasserstein GAN and real data sequences, Allen et al. [23] employed various metrics, including regression analysis, the application of moments and characteristic functions, and random forest analysis, in their paper GANs and Synthetic Financial Data: Calculating VaR. They also evaluated and applied the data by calculating the Value at Risk (VaR). To solve the problems of insufficient prior knowledge and high time complexity in urban master plan rendering, in response to the challenges of employing stochastic processes in financial time series modeling, Wiese et al. [24] introduced a data-driven Quant GANs model in their paper “Quant GANs: Deep Generation of Financial Time Series”. The model's generator ensures that the generated stochastic processes transition effectively to their risk-neutral distribution. Numerical experiments indicate that the distribution characteristics of the generated data closely align with those of real data. In exploring the applicability of deep generative models in the financial domain, Park et al. [25] propose a stock feature-based deep generative diffusion model in their paper Modeling Asset Price Process: An Approach for Imaging Price Chart with Generative Diffusion Models. This model effectively avoids prior assumptions about stock price movements, enabling a more accurate representation and generation of financial data. Experimental results demonstrate that the algorithm can successfully replicate well-known asset price processes, providing a novel approach for financial decision-making. Reinforcement learning models used in portfolio management have certain drawbacks, leading to suboptimal generalization results. In this regard, Kuo et al. [26] introduced an interactive generative adversarial model based on a limit order book to simulate financial markets in their paper Improving Generalization in Reinforcement Learning-Based Trading by Using a Generative Adversarial Market Model. The experimental results demonstrate that the framework improves out-of-sample portfolio performance by 4%, outperforming other generalization techniques.

2.2 Basis of Method Innovation

2.2.1 Generative Adversarial Networks

Generative Adversarial Networks (GANs) are a deep learning model consisting of a generator $G\left(z, \Theta_G\right)$ and a discriminator $D\left(x^*, \Theta_D\right)$, which follow the principles of zero-sum game theory, optimization theory, and Nash equilibrium. The generator $G\left(z, \Theta_G\right)$ is a neural network that generates synthetic samples $\bar{x}$ from noise z based on a prior distribution $p_z(z)$, aiming to make $\bar{x}$ as similar as possible to real data samples xx. The discriminator $D\left(x^*, \Theta_D\right)$ is a neural network designed to distinguish whether an input sample $x^*$ originates from the real data distribution xx or is a synthetic sample $\bar{x}$ generated by the generator. Here, $\Theta_G$ and $\Theta_D$ represent the parameters of the generator and discriminator, respectively. The value function is denoted as $V(G, D)$. Therefore, the Generative Adversarial Network can be formulated as follows:

$G\left(z, \Theta_G\right): \mathrm{z} \rightarrow \overline{\mathrm{x}}$      (1)

$D\left(x^*, \Theta_D\right): x^* \rightarrow[0,1]$      (2)

$\begin{aligned} \min _G \max _D V(D, G) & =E_{X \sim P_{\text {data }(x)}}[\log D(x)] \\ & +E_{z \sim P_{z(z)}}[\log (1-D(G(z)))]\end{aligned}$                  (3)

Eqs. (1)-(3) describe the Generative Adversarial Network (GAN) model and outline the improvement paths for the network.

2.2.2 Conditional Generative Adversarial Network

Conditional Generative Adversarial Network (cGAN) is a variant of Generative Adversarial Networks (GAN) that incorporates implicit conditions. By introducing a condition $c$ into both the generator $G\left(z \mid c, \Theta_G\right)$ and the discriminator $D\left(x^* \mid c, \Theta_D\right)$, cGAN achieves two key improvements: (1) The generator $G\left(z \mid c, \Theta_G\right)$ produces samples $\bar{x}$ that not only retain stochastic properties but also incorporate conditional attributes, enabling the generation of samples with specified features based on given conditions; (2) The discriminator $D\left(x^* \mid c, \Theta_D\right)$ performs authenticity verification of the sample $x^*$ based on the condition $c$, allowing for condition-dependent discrimination. The cGAN framework is described as follows:

$G\left(z \mid c, \Theta_G\right): z, c \rightarrow \bar{x}$      (4)

$D\left(x^* \mid c, \Theta_D\right): x^*, c \rightarrow[0,1]$       (5)

$\begin{aligned} \min _G \max _D V(D, G) & =E_{X \sim P_{\text {data }(x)}}[\log D(x \mid c)]+E_{z \sim P_{z(z)}}[\log (1-D(G(z \mid c)))]\end{aligned}$                (6)

$E_{X \sim P_{\text {data(x) }}}[\log D(x \mid c)]$ represents the discriminator's loss on real samples, indicating its ability to determine whether a real sample $x$ belongs to the true data distribution. $E_{z \sim P_{z(z)}}[\log (1-D(G(z \mid c)))]$ represents the discriminator's loss on generated samples, reflecting its ability to identify whether the generated sample $\bar{x}$ is fake. Therefore, the Conditional Generative Adversarial Network (cGAN) achieves optimal performance when the first term is maximized, and the second term is minimized.

2.2.3 Variational Autoencoder

A Variational Autoencoder (VAE) is a generative model based on probabilistic modeling in the latent space. The encoder $q(z \mid x)$ maps the input data $x$ to the latent space $z$, while the decoder $p(x \mid z)$ reconstructs the data $\bar{x}$ from the latent space $z$.

The VAE algorithm is described as follows:

$p(x, z)=p(x \mid z) p(z)$        (7)

$\begin{gathered}L(\theta, \phi ; x)=E_{q(z \mid x)}\left[\log p_\theta(x \mid z)\right]-K L((z \mid x) \left.\| p_{\varphi}(z)\right)\end{gathered}$                  (8)

Here, the data $x$ is generated through the latent variable $z$, where $p(x \mid z)$ represents the decoder, and $p(z)$ is the prior probability of the latent variable. The posterior distribution is denoted as $p(z \mid x)$, and the approximate distribution is $q(z \mid x)$. The term $E_{q(z \mid x)}\left[\log p_\theta(x \mid z)\right]$ represents the reconstruction loss, which quantifies the error in reconstructing data x from the latent variable z . The term $K L\left((z \mid x) \| p_{\varphi}(z)\right)$ is the KL divergence, which measures the difference between the variational distribution $q(z \mid x)$ and the prior distribution $p(z)$. Here, $\theta$ represents the decoder parameters, while $\phi$ denotes the encoder parameters.

2.2.4 Conditional vector projection

In the 2018 paper "Spectral Normalization for Generative Adversarial Networks", Miyato et al. proposed conditional vector projection (CVP), a technique for Conditional Generative Adversarial Networks (cGANs). This method is primarily applied to the discriminator $D\left(x^* \mid c, \Theta_D\right)$ to effectively incorporate conditional information, thereby improving the model’s discriminative capability and training stability. Conditional vector projection description:

$f(x)=D_{\text {feat }}(x)$       (9)

$p(y \mid x)=f(x)^{\top} v_y$      (10)

$D(x, y)=f(x)^{\top} v_y+b$      (11)

where, $D_{\text {feat }}(x)$ represents the feature extraction module of the discriminator. $f(x)$ is the feature representation of the input sample, $v_y$ is the learnable embedding vector corresponding to class $\mathrm{y}, p(y \mid x)$ introduces class information into the discriminator's decision function via inner product operation. b is a learnable bias term.

2.5 Self-attention mechanism

The self-attention mechanism is a window-sizeindependent method for learning long-range dependencies. It is widely used in Natural Language Processing (NLP) and Computer Vision (CV) tasks. Given an input sequence $X \in$ $R^{n \times d}$, where $n$ is the sequence length and $d$ is the feature dimension, the self-attention mechanism computes weighted relationships among Query $(Q)$, Key $(K)$, and Value $(V)$ to generate new feature representations, enabling the learning of long-range dependencies.

Table 5. Algorithm performance comparison